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Section 5.4 Adding and Subtracting Polynomials

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5.4 Lecture Guide: Adding and Subtracting Polynomials Objective 1: Use the terminology associated with polynomials. Monomials Polynomials Verbally A monomial is a real number, a variable, or a product of real numbers and variables with _______________ number exponents. A polynomial is a monomial or a sum of a finite number of _______________. Algebraic Examples – 5,, x, A, 5x, 7xy and are monomials. and are polynomials. is a polynomial.

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Binomial Trinomial Verbally A binomial is a polynomial containing _______________ terms. A trinomial is a polynomial containing _______________ terms. Algebraic Examples

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Degree of a Monomial The degree of a monomial is the sum of the _______________ for all the variables in this term. A nonzero constant is understood to have degree _______________ with exponent, but no degree is assigned to the monomial 0.

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1. Determine whether each expression is a monomial. If the expression is a monomial, give its coefficient and the degree of each monomial. Monomial? Yes / No Coefficient: ______ Degree: ______ Monomial? Yes / No Coefficient: ______ Degree: ______ Monomial? Yes / No Coefficient: ______ Degree: ______ Monomial? Yes / No Coefficient: ______ Degree: ______ (a)(b) (c) (d)

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2. Determine whether each expression is a polynomial. Classify each polynomial according to the number of terms it contains. (a) (b) (c) (d) Polynomial? Yes / No Polynomial? Yes / No Polynomial? Yes / No Polynomial? Yes / No Classification: ____________ Classification: ____________ Classification: ____________ Classification: ____________

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Standard Form of a Polynomial A polynomial is in standard form if (1) the variables in each term are written in ____________ order and (2) the terms are arranged in ____________ powers of the first variable. Degree of a Polynomial The degree of a polynomial is the same as the degree of the term with the ____________ degree. To find this highest degree, examine each term individually--- do not sum the degrees of the terms.

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3. Write each polynomial in standard form, and give the degree of each polynomial. (a) Standard form: Degree:

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3. Write each polynomial in standard form, and give the degree of each polynomial. (b) Standard form: Degree:

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3. Write each polynomial in standard form, and give the degree of each polynomial. (c) Standard form: Degree:

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Objective 2: Add and subtract polynomials. When adding or subtracting polynomials, remember to use the __________________ property to remove any grouping symbols and then add like terms. Remember that like terms have exactly the same ________ factors.

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Identify each pair of terms as like or unlike. 4.and 5. and

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6. Determine the sum or difference and write the result in standard form.

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7. Determine the sum or difference and write the result in standard form.

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8. Determine the sum or difference and write the result in standard form.

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9. Determine the sum or difference and write the result in standard form.

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10. Determine the sum or difference and write the result in standard form.

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11. Determine the sum or difference and write the result in standard form.

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12. Determine the sum or difference and write the result in standard form.

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13. Determine the sum or difference and write the result in standard form.

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14. The profit in dollars made by selling x units is given by the polynomial (a) Evaluate Evaluate and interpret each expression. Interpret

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(b) Evaluate Interpret 14. The profit in dollars made by selling x units is given by the polynomial Evaluate and interpret each expression.

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(c) Evaluate Interpret 14. The profit in dollars made by selling x units is given by the polynomial Evaluate and interpret each expression.

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15. Write a polynomial for the perimeter of the polygon.

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